Mathematical Programming Computation

, Volume 9, Issue 1, pp 61–100 | Cite as

Improved branch-cut-and-price for capacitated vehicle routing

  • Diego Pecin
  • Artur Pessoa
  • Marcus Poggi
  • Eduardo UchoaEmail author
Full Length Paper


The best performing exact algorithms for the capacitated vehicle routing problem developed in the last 10 years are based in the combination of cut and column generation. Some authors only used cuts expressed over the variables of the original formulation, in order to keep the pricing subproblem relatively easy. Other authors could reduce the duality gaps by also using a restricted number of cuts over the master LP variables, stopping when the pricing becomes prohibitively hard. A particularly effective family of such cuts are the subset row cuts. This work introduces a technique for greatly reducing the impact on the pricing of these cuts, thus allowing much more cuts to be added. The newly proposed branch-cut-and-price algorithm also incorporates and combines for the first time (often in an improved way) several elements found in previous works, like route enumeration and strong branching. All the instances used for benchmarking exact algorithms, with up to 199 customers, were solved to optimality. Moreover, some larger instances with up to 360 customers, only considered before by heuristic methods, were solved too.


Integer programming Column generation Cut separation Algorithmic engineering 

Mathematics Subject Classification

90C10 Integer programming 90C39 Dynamic programming 90C57 Polyhedral combinatorics branch-and-bound branch-and-cut 


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Copyright information

© Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society 2016

Authors and Affiliations

  • Diego Pecin
    • 1
  • Artur Pessoa
    • 2
  • Marcus Poggi
    • 1
  • Eduardo Uchoa
    • 2
    Email author
  1. 1.Departamento de InformáticaPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil
  2. 2.Departamento de Engenharia de ProduçãoUniversidade Federal FluminenseNiteróiBrazil

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